- Your homework on the Dimension unit will be returned Wednesday.
- You were to have read Section 4.5 for today.
- Part 2 (of 2) of your assignment for this Friday: Section 4.5, pp. 284-: #4, 5, 15
- One of the themes in Section 4.5 is that of symmetry. Beautiful symmetries of geometrical objects.
- In the plane of 2-Dimensions,
- What is the most symmetric rectangle?
- What are regular polygons?
- How many are there?
- What kinds of symmetry do they possess?
- Section 4.5: Platonic solids
The Five Convex Regular Polyhedra (Platonic solids) -- thanks Wikipedia! Tetrahedron Hexahedron
or CubeOctahedron Dodecahedron Icosahedron 
- Regular polyhedra start with regular polygons -- which ones play a role in the regular polyhedra?
- Now let's make them in 3-d: We're going to be using "geomags" today to
construct a set of Platonic solids (Problem I.1), and use them
to fill in the table on page 275:
# of Vertices Edges Faces faces at each vertex sides at each face Tetrahedron Cube Octahedron Dodecahedron Icosahedron What conclusions can we draw from this data? Is there a pattern?
- Why can't a hexagon be used to create a regular polyhedron?
- What kinds of symmetry do these objects possess?
- The concept of Duality
- Regular polyhedra start with regular polygons -- which ones play a role in the regular polyhedra?
- Links:
